Changing Behavior of Open Graphs

Discover what it means for intervals of a graph to be increasing, decreasing or constant.

Task 1

Task 2

What does it mean for a graph to be increasing over an interval? Decreasing? Constant?

Task 3

What can a graph look like when it is ONLY increasing? Decreasing? Constant?

Task 4

Is it possible for a graph to be both increasing and decreasing?

Task 5

Is it possible for a graph to be neither increasing nor decreasing?

Task 6

Can two intervals of a graph look different and yet both be increasing?

Task 7

What happens when two adjacent intervals of the graph exhibit the same behavior?

Task 8

Move the points so that part of the graph looks like a quadratic function. Over what intervals is it increasing, decreasing, or constant?

Task 9

Could the graph of an exponential function (like ) have intervals that are increasing, decreasing, or constant?

Task 10

How does the behavior of a quadratic function compare to the behavior of an exponential function?

Task 11

Can a function be increasing, decreasing or constant at a single point? Why or why not?